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# Previous Year Number System Questions for SSC Exams: Answers

Dear maths lovers, Let your practice begins in minuteness but ends in magnificence.It is impossible to study maths properly by just reading and listening. So, practise, practise & more practise. For that, we are providing here Quant Quiz of 15 Questions on Number System in accordance with the syllabus of SSC CGL.We have also provided Study Notes and quizzes on all the topics.

Q2. The LCM of two numbers is 40 times their HCF. The sum of the LCM and HCF is 1,476. If one of the numbers is 288, find the other numbers?
(a) 169
(b) 180
(c) 240
(d) 260

Q3. Four bells toll at intervals of 14, 21 and 42 minutes respectively. If they toll together at 11:22 am, when will they toll together for the first time after that?
(a) 11:56 am
(b) 12:04 pm
(c) 12:06 pm
(d) 11:48 am

Q4. If a number is divided by 15, it leaves a remainder of 7. If thrice the number is divided by 5, then what is the remainder?
(a) 5
(b) 6
(c) 7
(d) 1

Q6. How many zeros will be there at the end of 10 × 25 × 35 × 40 × 50 × 60 × 65
(a) 7
(b) 6
(c) 9
(d) 5

Q7. What is the unit digit of 576847 × 564068 × 96467 × 458576?
(a) 2
(b) 4
(c) 6
(d) 8

Q8. What is the unit digit of 1! + 2! + 3! + ……+ 99! + 100!?
(a) 3
(b) 1
(c) 5
(d) 6

Q9. How many divisors will be there of the number 1020?
(a) 12
(b) 20
(c) 24
(d) 36

Q10. How many zeros will be there at the end of the expression N = 2 × 4 × 6 × 8 × …… × 100?
(a) 10
(b) 12
(c) 14
(d) None of these

Q11. How many divisors of N = 420 will be of the form 4n + 1, where n is a whole number?
(a) 3
(b) 4
(c) 5
(d) 8

Q12. How many zeroes will be there at the end of 1003 × 1001 × 999 × …… × 123?
(a) 224
(b) 217
(c) 0
(d) None of these

Q13. A and B are two distinct digits. If the sum of the two-digit numbers formed by using both the digits is a perfect square, what is the value of (A + B)?
(a) 9
(b) 11
(c) 13
(d) 17

Q14. A number N = 897324P64Q is divisible by both 8 and 9. Which of the following is the value of P + Q?
(i). 2 (ii). 11 (iii). 9
(a) either (i) or (ii)
(b) either (ii) or (iii)
(c) either (i) or (ii) or (iii)
(d) None of these

Solutions

S2. Ans.(b)
Sol. Given, L.C.M = 40 H.C.F
l = 40 h
And,
l + h = 1476
41h = 1476 ⇒ h = 36
We know,
L.C.M × H.C.F = I no. × II no.
40h × h = 288 × x
40 × 36 × 36 = 288 × x
x = 180
Thus, the other no. 180

S3. Ans.(b)
Sol. LCM of 14, 21 and 42 is 42.
It means that after every 42 minutes all bells will toll together.
Then after 11:22 am they will toll at 11:22 + 42min = 11:64 = 12:04 pm

S6. Ans.(a)
Sol. (5 × 2) × (5 × 5) × (5 × 7) × (5 × 8) × (5 × 5 × 2) × (5 × 12) × (5 × 13)
No. of 5’s = 9
No. of 2’s = 7
Zero’s at the end = 7

S7. Ans.(a)
Sol. Multiply all the unit digits.
= 7 × 8 × 7 × 6
Thus, unit digit = 2.

S8. Ans.(a)
Sol. Unit digit of 1! +2! + 3! + 4! + 5! + 6! ………… = 1 + 2 + 6 + 24 + 120 + 0 ……… = 3
Note: We know that unit digit of 5! and for all the numbers greater than 5! = 0.

S12. Ans.(c)
Sol. Since all the numbers in the expression are odd.
So, the product of all odd numbers would also be odd.
Hence, the number of zeros is 0.

S13. Ans.(b)
Sol. It is given that AB + BA = perfect square
(10A + B) + (10B + A) = perfect square
11(A + B) = perfect square.
For being a perfect square, (A + B) should be 11.

S14. Ans.(a)
Sol. N = 897324P64Q
For N divisible by 8, the last three digits should be divisible by 8.
But 64Q is divisible by 8 when Q equals 0 or 8
And for N divisible by 9, the sum of digits should be divisible by 9.
Now if Q = 0, then P should be 2,
And if Q = 8, then P should be 3.
Then P + Q = 2 or 11.